We've got presents for you. - One may
give a present
to another person, but in this case you are saying that they
have presents which are intended
for the other person.
He was lying on the floor. - Many Americans will say
laying, however, to say that one is laying something down means that they are in the
act of laying something down, not that it is already in a horizontal position, a confusing idiosyncracy.
He used the crowbar to hook onto the window sill. -
Into implies penetrating or placing something inside something else.
He pulled himself ...... the walkway - I'm afraid I can't answer this until I know what the walkway is and its position.
He buried his hands in the snow
He continued to climb up with (remove "his") bare feet (two words) - This is a little clumsy. I would re-word it to say, "Barefooted, he continued to climb," or, "He continued to climb though his feet were bare"
He walked barefooted across the the snow covered backyard. - It just sounds better this way
The glue covered wrapping plastic stuck (not sticked) to his face. - Well it's not
in his face (unless he's eating it, I suppose

)! You could say it stuck on his face, but it sounds awkward.
He ..... over the rope. - All of these options are acceptable, it's up to you which word you'd like to use.
He ..... down with his bare feet (again, two words) on the ornament(al?) glass. I can't really answer this unless you tell me the context, 'stepped' and 'stomped' both work in the sentence, but they change it's meaning accordingly.